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arXiv · gr-qc/9708011

The Hilbert Action in Regge Calculus

Warner A. Miller
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Abstract

The Hilbert action is derived for a simplicial geometry. I recover the usual Regge calculus action by way of a decomposition of the simplicial geometry into 4-dimensional cells defined by the simplicial (Delaunay) lattice as well as its dual (Voronoi) lattice. Within the simplicial geometry, the Riemann scalar curvature, the proper 4-volume, and hence, the Regge action is shown to be exact, in the sense that the definition of the action does not require one to introduce an averaging procedure, or a sequence of continuum metrics which were common in all previous derivations. It appears that the unity of these two dual lattice geometries is a salient feature of Regge calculus.

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Warner A. Miller. 1997-08-06. The Hilbert Action in Regge Calculus. https://doi.org/10.1088/0264-9381%2F14%2F12%2F004

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